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Journal of Volcanology and Geothermal Research 137 (2004) 109–134

Acoustic measurements of the 1999 basaltic eruption

of Shishaldin volcano, Alaska

1. Origin of Strombolian activity

S. Vergniollea,*, M. Boichua, J. Caplan-Auerbachb,1

aLaboratoire de Dynamique des Systemes Geologiques, Institut de Physique du Globe de Paris, 4 Place Jussieu, Paris Cedex 05 75252, FrancebAlaska Volcano Observatory, Geophysical Institute, University of Alaska, Fairbanks, USA

Abstract

The 1999 basaltic eruption of Shishaldin volcano (Alaska, USA) displayed both classical Strombolian activity and an

explosive Subplinian plume. Strombolian activity at Shishaldin occurred in two major phases following the Subplinian activity.

In this paper, we use acoustic measurements to interpret the Strombolian activity.

Acoustic measurements of the two Strombolian phases show a series of explosions that are modeled by the vibration of a

large overpressurised cylindrical bubble at the top of the magma column. Results show that the bubble does not burst at its

maximum radius, as expected if the liquid film is stretched beyond its elasticity. But bursting occurs after one cycle of vibration,

as a consequence of an instability of the air–magma interface close to the bubble minimum radius. During each Strombolian

period, estimates of bubble length and overpressure are calculated. Using an alternate method based on acoustic power, we

estimate gas velocity to be 30–60 m/s, in very good agreement with synthetic waveforms.

Although there is some variation within these parameters, bubble length and overpressure for the first Strombolian phase are

found to be c 82F 11 m and 0.083 MPa. For the second Strombolian phase, bubble length and overpressure are estimated at

24F 12 m and 0.15 MPa for the first 17 h after which bubble overpressure shows a constant increase, reaching a peak of 1.4

MPa, just prior to the end of the second Strombolian phase. This peak suggests that, at the time, the magma in the conduit may

contain a relatively large concentration of small bubbles. Maximum total gas volume and gas fluxes at the surface are estimated

to be 3.3� 107 and 2.9� 103 m3/s for the first phase and 1.0� 108 and 2.2� 103 m3/s for the second phase. This gives a mass

flux of 1.2� 103 and 8.7� 102 kg/s, respectively, for the first and the second Strombolian phases.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Shishaldin; eruption dynamics; acoustics; Strombolian activity; bubble

1. Introduction

The most common explosive eruptive behaviours

observed for basaltic volcanoes are periodic fire

0377-0273/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jvolgeores.2004.05.003

* Corresponding author.1 Now at the Alaska Volcano Observatory, U.S. Geological

Survey, Anchorage, AK, USA.

fountains (Hawaiian activity) or regular explosions

(Strombolian activity). Both eruptive types are driven

by large gas pockets, with a size on the order of the

conduit radius for Strombolian explosions or much

longer for Hawaiian fire fountains (Vergniolle and

Jaupart, 1986). One characteristic feature is an alter-

nating between a phase rich in gas and a phase

relatively poor in gas (Jaupart and Vergniolle, 1988,

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134110

1989; Vergniolle and Jaupart, 1990). The formation of

the gas rich phase, i.e. a fire fountain for Hawaiian

volcanoes and regular explosions for Strombolian

volcanoes, is a consequence of small gas bubbles

rising in the reservoir. These bubbles rise and accu-

mulate at the top, where a foam layer builds. When

the foam reaches a critical thickness, it collapses

either totally for very fluid lava (Hawaiian case) or

partially for more viscous lava (Strombolian case).

The formation of a large gas pocket in the conduit

leads to a fire fountain or a Strombolian explosion

(Jaupart and Vergniolle, 1988, 1989; Vergniolle and

Jaupart, 1990).

Understanding eruption behaviour requires a clear

understanding of flow parameters, such as pressure

and velocity, variables which are necessary for mod-

elling the flow of magma and gas from depth to the

surface. Because it is obviously impossible to measure

these parameters directly, our best hope is to constrain

these values at the surface. For a long time, however,

the only estimates of physical parameters during

surface activity came from visual observations, such

as the height reached by ejecta (Blackburn et al.,

1976; Wilson, 1980; Wilson and Head, 1981) or from

studies of photoballistics (Chouet et al., 1974;

McGetchin et al., 1974; Ripepe et al., 1993). For

example, observations have been made of gas bubbles

breaking at the surface of volcanoes such as Heimaey

(Iceland) and Stromboli (Italy) (Self et al., 1974;

Blackburn et al., 1976; Wilson, 1980). Using esti-

mates of gas velocity, overpressure during Strombo-

lian activity was estimated at c 0.025 MPa for

Heimaey and at c 600 Pa for Stromboli (Blackburn

et al., 1976). Such measurements yield typical Strom-

bolian gas velocities of less than 100 m/s (Chouet et

al., 1974; McGetchin et al., 1974; Blackburn et al.,

1976), while gas velocities estimates for Hawaiian fire

fountains reach 100 or 200 m/s (Wilson, 1980; Wilson

and Head, 1981; Vergniolle and Jaupart, 1990). Direct

geophysical measurements of gas and ejecta veloci-

ties, during Strombolian activity, have confirmed

these values either by the use of a sodar (Weill et

al., 1992) or by a radar (Hort and Seyfried, 1998;

Dubosclard et al., 1999, in press) pointed towards the

active vent.

Until recently, measurements of acoustic waves

produced by an erupting volcano have been relatively

sparse. This is primarily due to the fact that for many

years low cost instruments could only measure audi-

ble frequencies (above 20 Hz) (Richards, 1963;

Woulff and McGetchin, 1976) and volcanic sound

waves are primarily infrasonic. Recent technologies

have allowed these frequencies to be recorded and

show that they can be used to estimate source char-

acteristics (Vergniolle and Brandeis, 1994, 1996;

Vergniolle et al., 1996; Hagerty et al., 2000). On

volcanoes, such as Stromboli (Buckingham and Gar-

ces, 1996) or Pavlof (Garces and McNutt, 1997), the

propagation of acoustic pressure in the shallow mag-

ma and its transport towards the atmosphere has been

calculated.

There are three main models that have been devel-

oped for volcanic acoustic signals. The first class of

acoustic models associates the frequency and ampli-

tude of acoustic signals with resonant modes of the

shallow volcanic conduit (Buckingham and Garces,

1996; Garces et al., 2000; Hagerty et al., 2000). While

useful for some volcanoes, a resonating conduit mod-

el, when applied to Stromboli, leads to extremely high

values of viscosity (9� 105 Pa s) and source over-

pressure (1�103 MPa) at shallow depth (Bucking-

ham and Garces, 1996). At Arenal volcano (Costa

Rica), an explosive source, buried at 12 m below the

surface and with an overpressure of 3.4 MPa produces

an excellent, although non-unique fit to the observed

acoustic waveforms (Hagerty et al., 2000).

The second class of acoustic models suggest that

sound is produced when the volcano is suddenly

uncorked after reaching a pressure threshold. Uhira

and Takeo (1994) suggest that the overpressure in the

source is at least 0.3 MPa at Sakurajima volcano

(Japan). For Johnson et al. (1998) and Johnson and

Lees (2000), Vulcanian explosions, corresponding to

the disruption of a plug at the top of the magma

column, are characteristic of a magma with interme-

diate viscosity, such as those seen at Karymsky

(Kamchatka, Russia), Sangay (Ecuador) and Arenal

volcanoes (Costa Rica).

In contrast, volcanoes with fluid lava, such as

Stromboli, Kilauea (Hawaii), Villarica (Chile), Erebus

(Antartica) keep an open vent through which large gas

bubbles can escape and burst (Sparks et al., 1997). In

this type of activity, sound is produced by the strong

vibration of a large cylindrical bubble prior to its

bursting at the top of the magma column (Vergniolle

and Brandeis, 1994, 1996; Vergniolle et al., 1996). At

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134 111

Stromboli, acoustic data have been used to determine

parameters such as bubble radius (c 1 m), length

(between 1 and 20 m) and bubble overpressure

(c 0.10 MPa) (Vergniolle and Brandeis, 1996). Be-

cause a bubble approaching an interface can develop

kinematic waves whose frequency depends on viscos-

ity, the bubble at Stromboli is also heard rising in the

uppermost few tens of meters of the conduit before

breaking (Vergniolle et al., 1996).

In this paper, we describe the 1999 basaltic

eruption of Shishaldin volcano (Alaska, USA) during

two Strombolian phases and quantify the source of

acoustic signals recorded at a distance of 6.5 km

from the vent. Acoustic data show a series of

explosions, the waveforms of which are surprisingly

similar to those recorded at Stromboli volcano.

Therefore, the sound wave produced by each explo-

sion is modelled, as for Stromboli, by the vibration

induced by residual overpressure inside the bubble,

prior to bursting at the magma surface. The best fit

between the model and the explosion waveforms

allows us to estimate bubble radius, length and

overpressure during the course of the eruption. We

Fig. 1. Location of Shishaldin volcano and Unimak Island, Alaska. Black c

the Alaska Volcano Observatory. The pressure sensor used to collect the ac

flank of Shishaldin. The two nearest population centers, False Pass and C

show that acoustic sensors, which can give very

good estimates on the gas velocity from acoustic

power, are both reliable and easy to implement for

volcanic monitoring.

2. Setting and materials

Shishaldin volcano is located on Unimak Island,

the first island in the Aleutian arc (Fig. 1). Its

historical eruptions have been primarily Strombolian

in nature, producing steam and moderate height ash

plumes of basalt and basaltic andesite. Rare instances

of andesite or dacite eruptions have also been noted

(Fournelle, 1988). Large volume tephra layers,

whose origin might be Subplinian, are seen with

an occurrence of 11 in the past 9 ka, whereas

classical basaltic eruptions occur with an intermit-

tency of c 20 eruptions/century (Beget et al., 1998;

Nye et al., 2002).

In 1997, a six-station seismic network was installed

near Shishaldin by the Alaska Volcano Observatory

(AVO) (Fig. 1). Five of the stations are short period

ircles represent the locations of the short-period network operated by

oustic data in this study is co-located with station SSLN on the north

old Bay, are marked with triangles.

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134112

Mark Products L-4C instruments with natural period

of 1 s. Station SSLS is a three component Mark

Products L-22 instrument with 0.5-s natural period.

A Setra 239 pressure sensor, with a theoretical sensi-

tivity of 0.36 mV/Pa, was co-located with station

SSLN on the volcano’s north flank and has recorded

signals without saturation.

In 1997, at the time that the pressure sensor was

deployed at Shishaldin, no calibration facility existed

at the University of Alaska Fairbanks (UAF). Conse-

quently, the instrument was nominally calibrated by

comparing its output to that of a calibrated Bruel and

Kjaer microphone (Garces et al., 2001, pers. com.). At

this time the sensitivity was found to be c 0.2 mV/Pa

a value used in an initial study of the pressure sensor

data (Caplan-Auerbach and McNutt, 2003). Unfortu-

nately, the reference microphone was only calibrated

at high frequencies (z 1 Hz), with uncalibrated sour-

ces used at lower frequencies. Attempts to calibrate

the instrument when it was retrieved in 2003 were

unsuccessful due to an apparent fault within the

pressure sensor. The instrument was subsequently

returned to Setra for calibration where it was con-

firmed to be operating at its theoretical sensitivity. The

theoretical transfer function for the pressure sensor,

telemetry system and digitizer is flat for frequencies

V 4 Hz (Fig. 2).

In the field, the pressure sensor was installed in a

plastic box and mounted on the wall of the fiberglass

hut in which batteries and electronics were also

housed. The reference port was covered with a pro-

phylactic membrane (M. Garces, highly pers. com.,

Fig. 2. Theoretical transfer function for the pressure sensor,

telemetry system and digitizer. Note that the response is flat for

all frequencies below c 4 Hz.

2003) so that the port was protected from dirt or snow.

A pipe from the active port (diameter of c 1 cm) ran

from the casing through the leeward wall of the hut,

where it was positioned c 15 cm above the hut

flange, directed toward the ground to further minimise

the effects of wind. The effect of the housing in

instrument response is unknown. However, we note

that while the specific values recorded by the pressure

sensor carry a small degree of uncertainty, this does

not affect our interpretation of the sequence of events

in the 1999 eruption. Data from all instruments are

telemetered to Cold Bay or King Cove and then to

AVO over analog telephone lines. Finally the data are

low-pass filtered with a corner frequency of 20 Hz and

sampled at 100 Hz with 12-bit resolution. Although

the anti-aliasing filter diminishes signal amplitudes at

high frequencies, this effect is minimal at frequencies

V 4 Hz, the frequency band in which most of the data

discussed here are found.

The greatest source of uncertainty with respect to

signals recorded by the pressure sensor is in discrim-

inating between volcanic signals and signals produced

by other sources such as wind. The nearest weather

station to Shishaldin is stationed in Cold Bay (Fig. 1),

over 90 km from the volcano. Moreover, it is likely that

a volcano the size of Shishaldin has a significant effect

on the local wind field. Consequently, wind conditions

at the pressure sensor site were unknown at the time of

the eruption. However, an unidentified low frequency

(0–3 Hz) signal bearing little to no resemblance to the

waveforms recorded at the time of the eruption was

commonly recorded on the pressure sensor. This signal

was observed both before and after the eruption,

suggesting that its source was non-volcanic, and pos-

sibly due to the wind. However, we were careful to

consider wind as a potential source for each of the

signals recorded during the eruption as well.

3. Eruption activity

Although tremor and satellite thermal anomalies

indicated unrest at Shishaldin as early as January

1999, the first confirmation of eruptive activity was

not made until April 18, 1999. At this time, AVO

researchers performed an overflight of the volcano.

Although a thick cloud obscured Shishaldin’s summit,

imagery acquired with a Forward Looking Infrared

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134 113

Radiometer (FLIR) shows the first confirmed spatter-

ing activity, with ejection of lava c several tens of

meters above the crater wall (Nye et al., 2002). After

30 h of apparent quiet, a series of tiny bursts were

detected by the pressure sensor. This phase, referred to

as the ‘‘hum’’ lasted 13 h and was followed by a

dramatic increase in seismic tremor accompanied by

an ash plume to heights above 16 km (Caplan-Auer-

bach and McNutt, 2003). This Subplinian eruption is

believed to be responsible for the majority of ejecta

produced by Shishaldin in 1999 (Stelling et al., 2002).

The Subplinian phase was immediately followed by

the first major Strombolian phase, lasting 3.5 h.

Explosions recorded during this phase have mean

frequencies near 0.7–0.8 Hz and mean amplitudes

of 1–2 Pa at 6.5 km from the vent. Two small bursts

of Strombolian activity occurred 2 and 7 h after the

first major Strombolian phase. Because these corre-

spond to bubbles just at the limit of detection and they

occurred for only a short time ( < 1 h), they will be

ignored here. After 60 h of quasi-quiescence, the

second Strombolian phase began and lasted almost

24 h (April 22–23, 1999). These events have power

spectral peaks near 1.1–1.5 Hz. For the first 17 h of

this phase, explosions have amplitudes of 0.5–4 Pa.

During the final 4 h of this phase, acoustic pressure

increased dramatically, with peak amplitudes exceed-

ing 30 Pa (Caplan-Auerbach and McNutt, 2003).

After this Strombolian phase, the eruption decreased

in intensity. However there were several ash plumes in

April (23rd, 26th) and May (13th, 25th, 26th) before

the eruption definitively ended.

Most of the following interpretation of the erup-

tion is based on data from the pressure sensor, co-

located with station SSLN at 6.5 km from the vent

(Fig. 1). The first acoustic signals that can be

definitively associated with the eruption were

recorded after the observed spattering activity on

April 18, 1999. All of the nearest seismic stations,

including the station co-located with the pressure

sensor (SSLN; Fig. 1), were saturated by strong

tremor during most of the eruption, making it diffi-

cult to directly compare seismic and acoustic signals

(Caplan-Auerbach and McNutt, 2003). The other

seismometers provide qualitative information on the

frequency spectra inside the volcanic edifice. All this

information is combined to produce a complete

understanding of the 1999 Shishaldin eruption, de-

spite the difficulties associated with accessing such a

remote site. In this first paper, we shall discuss the

two Strombolian phases and estimate gas volume

and pressure at the vent. In a series of papers, we

interpret the pre-Subplinian (Vergniolle and Caplan-

Auerbach, 2004a, this issue), trends in gas velocity

(Vergniolle and Caplan-Auerbach, 2004b), the Sub-

plinian phase (Vergniolle and Caplan-Auerbach,

2004c) and propose a general mechanism to explain

the chronology of the entire 1999 Shishaldin erup-

tion (Vergniolle and Caplan-Auerbach, 2004d).

4. Bubble vibration model

During Strombolian activity, the gas pocket is

released by foam coalescence at depth and rises in

the volcanic conduit. Its violent formation at depth

causes an excess of pressure inside the large bubble,

resulting in strong initial oscillations (Vergniolle,

1998). The bubble takes a finite time to rise through

the conduit, and its motion might be expected to

generate acoustic or seismic energy. However, at

Shishaldin, the frequent bursting of bubbles at the

surface, with inter-event times of less than 10 s,

prohibits us from identifying the low amplitude sig-

nals associated with bubble rise. Furthermore, the

seismic traces were saturated by strong seismic trem-

or, so seismic signals resulting from bubble rise are

also impossible to distinguish. Due to the large liquid

viscosity, the long newly formed bubble, rising in a

conduit, does not have enough time to equilibrate its

internal pressure to the decreasing pressure field

(Vergniolle, 1998). When it reaches the top of the

magma column, an excess of pressure is kept inside

the ‘‘about to break’’ bubble and strong volumetric

oscillations at the magma surface ensue. The ampli-

tude of oscillations results in the radiation of sound

waves (Vergniolle and Brandeis, 1996; Vergniolle,

2003). The extreme similarity between the waveforms

for explosions recorded at Stromboli and Shishaldin

volcanoes suggests that the same mechanism is at

work (Fig. 3).

4.1. Qualitative description

Bubbles of several meters in diameter have been

observed bursting at the vent at Etna (Coltelli et al.,

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134114

1998; T. Pfeiffer’s photograph, pers. com., 2001).

However, the bursting, i.e. the connection of magmat-

ic gas to atmosphere, of such large bubbles produces

frequencies around 150 Hz for a radius of 1 m and 30

Hz for a radius of 5 m by analogy to the balloon

bursting problem (Temkin, 1981; Vergniolle and

Brandeis, 1994). Because frequencies recorded at

Shishaldin volcano are c 1 Hz, we propose that its

sound is produced by the vibration of a shallow metric

bubble prior to bursting, rather than by the popping

noise (Vergniolle and Brandeis, 1994, 1996). Any

bubble in an infinite liquid oscillates easily: inertia

causes the bubble to overshoot its equilibrium radius

and the compressibility of gas, through the internal

gas pressure, acts like a restoring force (Batchelor,

1967; Leighton, 1994). The experimental study of

Kirpatrick and Lockett (1981) indicates that bubbles

moving at speeds approaching the terminal velocity

upon reaching the free surface, tend to come to rest

and bounce a couple of times before bursting. Here,

Fig. 3. Time series for Strombolian explosions at (a, b) Shishaldin and (c)

between the two waveforms encourages us to apply the same acoustic mod

Shishaldin and c 9 Hz at Stromboli. Data in figure a are raw and the m

since the bubbles are coming from the depth of the

reservoir, their rise speed had enough time to reach its

equilibrium value and the bubble vibration at the top

of the magma column, which is the volume mode, is

the most likely phenomenon to explain the peak in

acoustic pressure. Here, we assume that the oscilla-

tions are set up by a sudden overpressure inside a

large bubble reaching the magma–air interface.

We approximate the bubble shape by a hemispher-

ical head and a cylindrical tail, as expected in slug-

flow (Fig. 4). If the lava is close to the surface, as it is

the case at Shishaldin (Dehn et al., 2002), no external

limitation exists on bubble growth when the bubble

reaches the surface and breaks in the much larger area

of the crater (Fig. 5).

Although most vents are seen to be funnel shaped

(Sparks et al., 1997), the precise shape of the vent at

Shishaldin is not well known, and thus we do not

consider its exact geometry. We also neglect the

amplification of the sound inside a short tube and

Stromboli. E marks where explosions occur. The extreme similarity

el for both volcanoes. Note that frequencies are different, c 1 Hz at

ean value of acoustic pressure is removed in figure b.

Fig. 5. Two photographs of Shishaldin vent taken by P. Stelling

(AVO) during an overnight flight of the 16 August 1999. The radius

of the conduit mouth was estimated in 2003 by using the shadow of

the helicopter on the ground next to the crater.

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134 115

the distortion due to its propagation from the source to

the microphone, as we have shown they are small

when recording close to the source (Vergniolle and

Brandeis, 1994, 1996). At Shishaldin, there is line-of-

sight viewing from the summit to the location of the

pressure sensor, and the crater wall is lower in that

direction, allowing direct acoustic propagation.

While we cannot rule out the possibility of echoes

from the crater walls, the extreme similarity between

Shishaldin explosive signals and those observed at

other volcanoes suggests that echoes did not contrib-

ute significantly to the time series. At the time of

Strombolian activity, thermal anomalies in satellite

imagery confirm that there was a significant amount

of lava within the summit crater (Dehn et al., 2002),

suggesting that the bubbles burst near the top of the

conduit, and thereby minimising the effects of prop-

agation within the conduit itself.

Because the distance between vent and measure-

ments site is relatively large, about 20 times the

wavelength, we have to consider the effects of the

propagation of the sound wave in a stratified atmo-

sphere. Because the atmosphere is stratified, the sound

speed varies with height and there are regions, at 10–

20 and 70–90 km elevation, in which the sound speed

is minimum (Garces et al., 1998a,b). These regions can

trap waves and propagation occurs along these ducts

without the radial attenuation of a monopole. At

Shishaldin, we are concerned with acoustic waves

generated at an elevation of 2.85 km above sea level

and recorded at 6.5 km. Therefore, a spherical wave

reaching the pressure sensor, can attain a maximum

height of 9.25 km into the atmosphere, well below the

low-velocity zones. Although the addition of a wind

Fig. 4. Sketch of a vibrating bubble at the top of a magma column.

R, L and h are, respectively, bubble radius, length and thickness of

the magma layer above the bubble.

field introduces anisotropy in the infrasonic propaga-

tion, a wind blowing opposite to the direction of the

wave propagation is simply to reduce the effective

sound speed (Garces et al., 1998a,b). Since we will

show in next section that the sound speed is c 340 m/s

and the radiation approximately that of a monopole, we

feel confident that atmospheric effects are not signif-

icant. Finally, the aforementioned similarity between

Shishaldin explosions and acoustic signals recorded at

Stromboli, Etna, Erebus and other volcanoes is a

compelling reason to believe that the waveforms are

not significantly affected by wind or atmosphere.

A Strombolian bubble reaching the surface is half

way immersed into the magma and half way in air,

despite a thin layer of magma above it (T. Pfeiffer’s

photograph, pers. com., 2001; Fig. 4). Because of the

large difference in viscosity between air and magma,

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134116

the motion of the immersed part of the bubble is

restricted (Vergniolle and Brandeis, 1994, 1996).

Therefore, bubble vibration is entirely concentrated

into its hemispherical cap: the magma–air interface

vibrates as the bubble does. The thickness of the layer

of magma is likely to be of the order of magnitude of

the average diameter of the ejecta, as observed on

large bursting bubbles. Ejecta, usually a few centi-

meters thick, are much smaller than the radius of the

bubble, which is on the order of 1–5 m (Vergniolle

and Brandeis, 1994, 1996). Hence, we will consider

this layer as a membrane. The temperature inside the

bubble is chosen to be 1323 K (the approximate

temperature estimated by Dehn et al. (2002) at the

time of Strombolian activity) and the magma will be

assumed Newtonian. To estimate the viscosity of

Shishaldin magmas, we use geochemical data from

Stelling et al. (2002)and Kware magma software

(Wohletz, 2001). Using a temperature of 1323 K

and a water content of 1.5 wt.% we estimate a

viscosity of 500 Pa s. Neither uncertainties on the

temperature or viscosity plays a major role in the

bubble dynamics at the air–magma interface.

4.2. Equations

The source of sound is a thin layer of magma,

pushed by a variation of internal pressure inside the

bubble (Vergniolle and Brandeis, 1996). We have

shown for Stromboli that the source is a monopole

as its amplitude decreases inversely proportional to

the distance between the microphone and the vent

(Vergniolle and Brandeis, 1994). Similar analysis at

Shishaldin is not possible since the network includes

only a single pressure sensor. However, we examined

the amplitude of ground-coupled airwaves on the

Shishaldin seismic network and found that, to first

order, the amplitudes of these waves are inversely

proportional to distance from the vent. So we feel

confident that these explosions are also monopolar

and do not propagate into one of the ducted channels

of the stratified atmosphere. In this case, the excess

pressure depends on the rate of mass outflow from the

source, q (Lighthill, 1978). Acoustic pressure pacemitted at the source at time t will reach the micro-

phone, at a time t+ r/c, where r is the distance r from

the vent and c the sound speed in air equal to 340 m/s,

as determined by the moveout of airwaves arriving at

the various Shishaldin seismic stations. For such a

radiation, analogous to a monopole, the excess pres-

sure pac� pair at time t is (Lighthill, 1978):

pac � pair ¼qðt � r=cÞ

4pr

¼ d2

dt24pR3ðt � r=cÞ

6

� �qair

2prð1Þ

where qair is air density equal to 0.9 kg/m3 at an

elevation of 2850 m (Batchelor, 1967). Note that

factor 2 in the farthest right hand-side of the equation

accounts for radiation in a halfspace, whereas a factor

of 6 represents half a spherical bubble. Therefore,

acoustic pressure is exactly that of a monopole.

The bubble vibrates as a thin membrane of thick-

ness h. Its head grows but remains spherical with a

radius R, the normal mode being assumed for sim-

plicity and favored during the bubble expansion. The

part of the bubble which remains in the cylindrical

tube has a length L (Fig. 4). Hence, the bubble has a

volume Vg equal to:

Vg ¼2pR3

3þ pR2

oL ð2Þ

where Ro is the initial radius. Note that in the

following, indexes o, g and eq refer to initial con-

ditions, gas and equilibrium values, respectively. The

high viscosity of magma impedes any significant

drainage by gravity of the magma above the bubble,

during the short time allowed for the bubble to

vibrate. The volume of magma above the bubble is

conserved and the liquid stretches, following the

variations in bubble radius:

R2h ¼ R2eqheq: ð3Þ

Because heat transfer inside large bubbles is adia-

batic (Plesset and Prosperetti, 1977; Prosperetti, 1986),

the pressure pg inside the bubble follows the variations

of its volume Vg with a ratio of specific heat c, equal to1.1 for hot gases (Lighthill, 1978). Suppose, for sim-

plicity, that the bubble, initially at rest at the magma–

air interface, is suddenly overpressurised by an amount

DP. The bubble starts to grow and vibrate in response to

the pressure change. Pressure and volume obey the

adiabatic law, hence we can follow their variations. The

bubble radius R can be expressed by its variation

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134 117

around its equilibrium radius Req calculated from the

initial conditions and the adiabatic law (Vergniolle and

Brandeis, 1996):

R ¼ Reqð1þ eÞ ð4Þ

with

Req ¼3

2

� �1=32R3

o

3þ R2

oL

� �1þ DP

pair

� �1=c

�R2oL

" #1=3:

ð5ÞThe motion of the bubble is possible through an

exchange between the kinetic energy of its hemispher-

ical cap and the potential energy inside the gas and the

general equation for bubble vibration is:

e þ 12lqliqR

2eq

!e þ pair

qliqReqheq1� Veq

Vg

� �c� �ð1þ eÞ2

¼ 0 ð6Þ

where the gas volume Vg is a function of e (Vergniolleand Brandeis, 1996). Finally, we have to specify two

initial conditions. The first one is the initial radial

acceleration eo, which depends on the initial force

applied to the layer of magma. Assuming that the

bubble, at rest at the magma–air interface, is suddenly

overpressurised by an amount DP, this force is directly

related to the bubble overpressure. Since the bubble is

formed at depth and rises in a tube full of viscous

liquid, there is always an disequilibrium between the

external pressure field and the gas pressure as a

consequence of the significant delay to equilibrate a

moving bubble with large viscosity fluids (Vergniolle,

1998, 2001). Therefore, the overpressure at the sur-

face can be viewed as a consequence of either the

bubble rise within a viscous magma or its violent

formation at depth (Vergniolle, 1998, 2001).

The initial radial acceleration, eo is equal to:

eo ¼DPR2

o

qliqR3eqheq

: ð7Þ

The second initial condition to be specified is the

initial radius eo:

eo ¼Ro

Req

� 1: ð8Þ

Radial acceleration is maximum when the strong

vibration starts and, therefore, the initial radial veloc-

ity is equal to zero. These initial conditions corre-

spond to a bubble close to its minimum radius.

Bubble radius, velocity and acoustic pressure are

calculated for a typical bubble present during the

initial period of the second Strombolian phase. For a

bubble radius of 5 m, a length of 24 m and an

overpressure of 0.15 MPa, the maximum velocity is

30 m/s (Fig. 6). The magma above the bubble starts

with a thickness of 0.8 m when the oscillation is set up

into the bubble and reaches a minimum at 0.08 m.

Damping due to the viscosity, l = 500 Pa s, is very

small (Fig. 6c). The first absolute minimum in acous-

tic pressure corresponds to the maximum bubble

expansion (Rc 15.4 m) and the second following

zero in acoustic pressure to the minimum radius (Fig.

6d). Note that the non-linearity of the equations result

in an asymmetry between the positive and the nega-

tive peak and that acoustic pressure, which depends

on acceleration as well on velocity, is at its minimum

close to the maximum radius.

The bubble vibration can have a large amplitude and

cases are reported where maximum radius is twice the

equilibrium radius when the bubble collapse, occurring

near its minimum radius, is modelled (Leighton, 1994).

Here, at Shishaldin, although the change in bubble

radius is large, the maximum radius, c 15.4 m, is less

than twice the equilibrium radius, c 11.3 m during the

second Strombolian phase (Fig. 6a).

4.3. Description of the model

Direct observations of large bubbles at the top of

the magma column are very sparse because the lava is

rarely visible at the vent and because viewing such

activity is typically dangerous. Although Blackburn et

al. (1976) report some bubbles at Heimaey and

Stromboli, the short duration of the bubble vibration

cycle at the interface, probably between 0.1 and 1 s,

makes identification of this vibration difficult at best.

Furthermore, the large bubbles present during Strom-

bolian activity are probably of two different types.

Strombolian bubbles are those which form in the

magma chamber and consequently arrive at the top

of the magma column with some residual overpres-

sure. These are strongly overpressurised, break while

producing large ejecta velocities and cannot be safely

Fig. 6. Time evolution for a characteristic bubble of initial radius R0 = 5 m, length L= 24 m, overpressure DP= 0.15 MPa, equilibrium thickness

above bubble heq = 0.15 m, l = 500 Pa s. Oscillations start at time equal to 0.4 s. (a) Bubble radius (m). (b) Bubble radial velocity (m/s). (c)

Bubble velocity (m/s) as a function of bubble radius (m). (d) Acoustic pressure recorded at 6.5 km from the vent (Pa).

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134118

observed. The second type of large bubble corre-

sponds to those formed by local and slow coalescence

in the conduit, and has no significant overpressure at

the top of the magma column. Although they are

difficult to see on acoustic records, due to their lack of

gas overpressure, they may correspond to the bubbles

observed popping at the vent, which are safe to

observe.

Our model for the sound produced at the vent

during the Strombolian phases is based on the

assumption that the large bubble, lying just below

the top of the magma column, is suddenly set with

an initial gas overpressure at time t equal zero.

Although this assumption is a simplification, once

the bubble rises from depth, its internal pressure is

never at its equilibrium because the bubble is con-

tinuously exposed to a lesser external pressure and

the viscosity of the liquid delays the return to

equilibrium (Vergniolle, 1998, 2001). As the bubble

approaches the top of the magma column, the

pressure release increases on the gas inside the

bubble, leading to the build-up of a viscous over-

pressure inside the large bubble (Vergniolle, 1998).

Furthermore the formation of the large bubble at the

depth of the reservoir from foam coalescence (Jau-

part and Vergniolle, 1988, 1989) is violent and an

initial overpressure is set in the bubble when it starts

rising in the conduit (Vergniolle, 1998). At Strom-

boli, the initial overpressure at the approximate depth

of 300 m, is of the order of 11 MPa (Vergniolle,

1998) in agreement with seismic studies (Chouet et

al., 2003). However calculations of the exact phys-

ical behaviour of the large bubble close to the top of

the magma column are very complex and are left to

further studies.

There are many papers which discuss the behaviour

of a pulsating bubble in a infinite liquid (Leighton,

1994). Our equations are fairly similar to Rayleigh-

Plesset equations (Plesset and Prosperetti, 1977;

Prosperetti, 1986; Leighton, 1994), although they

are adapted for the vibration of a bubble close to

an interface between a liquid (magma) and a gas (air

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134 119

at atmospheric pressure). In these papers, the scaling

for the oscillation amplitude is done on the bubble

maximum radius, but our scaling on its equilibrium

radius is strictly equivalent (Eq. (4)). A bubble

pulsating at finite amplitude, as here with the max-

imum dimensionless radius ec 0.36 (Eq. (4)), is

clearly a non-linear oscillator as shown by its trajec-

tory phase (Fig. 6c). There is an obvious asymmetry:

while in expansion the amplitude of the bubble wall

displacement has no absolute limit, in compression

the radial displacement of the wall from equilibrium

cannot be greater than the equilibrium radius

(Leighton, 1994). Surface tension and viscosity have

a significant effect on the dynamics of microbubbles

but are less effective in maintaining a spherical shape

for the large Strombolian bubbles described here.

Consequently, the bubbles experience shape distor-

tions and oscillations due to overshooting (Leighton,

1994). At Shishaldin, the shape of the large bubble is

confined by the conduit walls to be cylindrical with

a nose whose shape results from the potential flow of

liquid around its tip (Batchelor, 1967; Wallis, 1969).

Furthermore, the large viscosity of the magma

around the bubble slows down the potential defor-

mations and the initial overpressure, existing in the

bubble once oscillations are set, favors a spherical

bubble cap during its expansion.

Large bubbles have been produced by underwater

chemical explosions using explosive charges and the

largest charge can generate a bubble with a maximum

radius of 10 m. The maximum radii of bubbles

produced by underwater nuclear explosions are of

the order of 100 m (Leighton, 1994). After expanding

to their maximum size as a result of an explosion, the

bubbles oscillate at least for several cycles before

reaching the sea surface (Batchelor, 1967; Leighton,

1994). For underwater explosions, the resulting bub-

ble oscillates for a few cycles between a minimum

radius of 5 m and a maximum of 18 m (Cole, 1948).

We envision a similar mechanism for Shishaldin

bubbles, although there the origin of oscillations is

obviously quite different.

Our model assumes that the magma above the

bubble has a constant volume during the duration of

one cycle, i.e. c 1 s. However, the thin liquid film

above the bubble is both pulled down by gravity and

slowed down by the viscous force within the film of

magma. For simplicity and although the bubble nose

is half a sphere, we assume that the flow occurs on a

vertical wall by gravity, providing a maximum bound

on the drainage velocity Vdr. The free fall of a thin

liquid film of thickness d onto a vertical solid wall has

a velocity of (Wallis, 1969):

Vdr ¼qliqgd

2

3lð9Þ

where lc 500 Pa s is the magma viscosity at

Shishaldin and qliqc 2700 kg/m3 the magma density.

The characteristic drainage time sdr is the ratio be-

tween the characteristic bubble radius Roc 5 m and

the drainage velocity based on the equilibrium thick-

ness dc heq:

sdr ¼Ro

Vdr

: ð10Þ

Although the drainage velocity is largely overesti-

mated, the drainage time sdr is larger than 12.6 s for anequilibrium thickness heq = 0.15 m. This is one order

of magnitude above the characteristic time for vibra-

tion, c 1 s, confirming that drainage is therefore

negligible during the bubble vibration at the top of

the magma column.

Acoustic measurements suggest that a Strombolian

bubble sustains one cycle of oscillation before break-

ing. This is possible if the radial stress rrr and the

tangential stresses rhh and r// do not exceed the

mechanical strength of the magma. For a bubble of

radius Ro surrounded by a thin magma shell of

thickness heq, the stresses are:

rrr ¼ DPg=2 ð11Þ

and

rhh ¼DPgRo

2heqð12Þ

where DPg is the gas overpressure (Landau and Lif-

shitz, 1986), here assumed to be equal to the initial gas

overpressure, DP. The smallest of the three stresses are

the tangential ones, equal to 25 MPa, for the maximum

overpressure recorded during the two Strombolian

phases, c 1.4 MPa, a bubble radius of 5 m and a film

thickness of 0.15 m. Because the tensile strength of

magma, 320 MPa (Dingwell, 1998), is more than 10

times larger than the applied stress, the magma layer

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134120

above the Strombolian bubbles at Shishaldin is me-

chanically stable and will not fail. Therefore, the

bubble can vibrate and does not pop. The model of

bubble vibration before breaking is in excellent agree-

ment with the measured frequency, which is more than

an order of magnitude below the frequency of a

bursting balloon, i.e. a bubble whose liquid film is

stretched beyond its elasticity towards bursting. Fur-

thermore, the simplified model for a balloon bursting

produces a waveform of the acoustic pressure, which

corresponds to a N-Wave, i.e. with both a very strong

rising time and the same amplitude for the positive and

negative peaks (Temkin, 1981). These two features are

not observed in the Shishaldin acoustic record.

The second mechanism by which such a large and

overpressurised bubble can break is by developing

instabilities at the magma–air interface or the mag-

ma–bubble interface. If the gas–liquid interface is a

plane surface, the interface is stable only when the

Fig. 7. (a) Stability of the bubble wall interface and (b) bubble radius (m) i

initial bubble radius R0 of 5 m, bubble length of 24 m and initial overpres

magma viscosity l is 500 Pa s. Oscillations start at time equal to 0.4 s and t

i.e. around the minimum radius.

acceleration is directed from the liquid to the gas phase.

However, the stability of a spherical surface depends

not just on its acceleration but on its velocity: during

bubble growth the streamlines diverge and produce a

stabilising effect, while the reverse happens during

contraction (Plesset and Mitchell, 1956; Leighton,

1994). Although the bubble nose is only half a sphere,

we use the stability analysis for a sphere and the bubble

wall interface is stable if the stability factor CRT:

CRT ¼ ðn� 1Þðnþ 1Þðnþ 2ÞrqliqRo

� 3R

4R2o

� ð2nþ 1ÞR2R0

ð13Þ

is greater than zero. n is the order of the harmonic, r the

surface tension, Ro, R and R are, respectively, the

bubble radius, bubble radial velocity and bubble radial

acceleration (Plesset and Mitchell, 1956; Leighton,

n time (s) for a typical bubble of the second Strombolian phase, with

sure of 0.15 MPa. Magma thickness above bubble heq is 0.15 m and

he bubble wall interface is unstable if the coefficient CRT is negative,

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134 121

1994). The surface tension term, with rc 0.36 kg/s2

for a basaltic magma at 1200 jC and 0.1 MPa (Prous-

sevitch and Kutolin, 1986; Proussevitch and Sahagian,

1996), can be ignored for bubbles as large as a few

meters. The perturbation of a spherical surface would

remain small for 1zR/RmaxV 0.2 and will become

violent for RVRmax/10. For a typical bubble of the

second Strombolian phase, of radius, length and over-

pressure of respectively 5 m, 24 m and 0.15 MPa, the

bubble is potentially unstable for about 1 s around its

minimum radius (Fig. 7). Although the bubble also

appears unstable for the first 0.4 s, this is a consequence

of assuming that the bubble oscillation is set at time

zero by a sudden overpressure. The ratio between the

minimum and the maximum radius, c 0.3, shows that

the instability, occurring close to the minimum radius,

is mild for Shishaldin bubbles. Although viscous

effects will delay the growth of the instability occurring

on the bubble wall near its minimum radius, acoustic

data shows that the bubble vibration probably lasts just

slightly more than one cycle.

Fig. 8. Comparison between measurements of acoustic pressure

(plain line) and synthetic waveform (dashed line) for one explosion

of the second Strombolian phase. The synthetic acoustic pressure is

produced by a bubble of radius R0 = 5 m, length L of 43 m and an

overpressure DP of 0.27 MPa. Bubble bursting probably occurs

after one cycle of vibration.

5. Generation of synthetic waveforms

Two main periods of Strombolian activity at

Shishaldin volcano were recorded by the pressure

sensor: on April 19 from 20:26 h to midnight (first

Strombolian phase) and from 12:00 h the 22nd of

April to 12:00 h the 23rd of April (second Strombo-

lian phase). During the quiet period in between,

some signals, also attributed to breaking bubbles,

were detected (Thompson et al., 2002; Caplan-Auer-

bach and McNutt, 2003) but are ignored here due to

poor signal strength.

Due to the enormous quantity of explosions, we

selected the largest explosion during a given time

period for waveform modelling. This period was taken

as 400 s for the first Strombolian phase and 800 s for the

second one, for a total of 29 and 106 analysed explo-

sions respectively. For each selected explosion of the

two Strombolian phases, a best fit between a synthetic

waveform and acoustic measurement is performed

manually. In generating synthetic waveforms there

are four parameters that are adjusted to determine the

best fit model: bubble radius, magma film thickness,

bubble length and bubble overpressure. Of these

parameters, we choose to fix the values for bubble

radius and magma film thickness at 5 and 0.15 m,

respectively, allowing bubble length and overpressure

to vary. The comparison between model and data is

extremely good for the first cycle of bubble vibration

and is not valid after the bubble bursts (Fig. 8). Here,

we discuss the assumptions associated with these

parameters and the effect on our results of varying

them.

5.1. Thickness of the magma layer, heq, above bubble

In previous studies of Strombolian explosions, the

thickness of magma above the vibrating bubble, heq,

has been scaled by the average diameter of ejecta

(Vergniolle and Brandeis, 1996). Photographs of

magmatic bubbles breaking at the surface of magma,

are in very good agreement with this assumption. At

Stromboli, this has lead to very reasonable values of

bubble overpressure, and length, between 2 and 20

times the bubble radius, as expected for slug flow

(Wallis, 1969). At Etna, a value of heq = 0.1 m gives

very reasonable results for the bubble length and

overpressure (Vergniolle, 2003). Shishaldin deposits,

however, yield few clues as to the size of the Strom-

bolian ejecta. Maximum clast sizes in Shishaldin

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134122

tephra samples range from 0.5–22 cm (Stelling et al.,

2002), but no distinction can be made between depos-

its ejected during the Strombolian and Subplinian

phases. Synthetic waveforms, however, suggest that

a value of 0.15 m is appropriate for Shishaldin

explosions, an approximation that we investigate

below.

Since we have little information on the size of

Strombolian ejecta, and hence the thickness of the

magma layer above the bubble, we assume that the

equilibrium thickness is the same for all bubbles

during the two Strombolian phases. Synthetic wave-

forms are very sensitive to the thickness of magma

above the breaking bubble because it represents the

mass of the oscillator. At Shishaldin, using a thick-

ness of magma outside of the range 0.1–0.2 m leads

to unreasonable values of either bubbles length and

overpressure. For example, a typical explosion of the

second Strombolian phase can be fit by using a film

thickness of 0.15 m and a bubble radius, length and

overpressure of respectively 5 m, 24 m and 0.15

MPa (Fig. 6). If the film thickness is doubled, the

bubble radius and length are halved to 2.5 and 10 m,

respectively. However, the initial overpressure is

multiplied by 6, giving 0.9 MPa at the vent, which

is more typical of an explosive volcano than one

with an open conduit. Thus, a 0.30 m thick film

would require unrealistic overpressures for this

phase. Secondly, the radial oscillation of the bubble

cap can only be excited when the thickness of the

liquid above the bubble is small compared to its

radius, so the bubble can produce a dome over the

liquid. For a film of equilibrium thickness of 0.3 m,

the magma thins from 1.5 to 0.11 m for a bubble

radius of only 2.5 m (Fig. 9) invalidating the

requirement that the film is small compared to the

bubble radius.

Finally, although a thickness heq equal to 0.2 m

matches most of the explosions, it failed for the

relatively ‘‘highest’’ frequencies measured on the

23rd of April. A value of heq equal to 0.1 m can

produce a reasonable match between synthetic

waveforms and measurements but leads to extremely

long bubbles, of a length above 20 times the radius.

We have no observations favouring extremely long

bubbles, since fire fountaining was not observed

during the Strombolian phases. Therefore, a value

of 0.15 m for the magma thickness above each

bubble, heq, is chosen for all explosions at Shishal-

din volcano.

Because the bubble breaks when its radius is close

to its minimum value, the liquid film is at its largest,

with a value close to 0.8 m when the bubble breaks.

However, since the mechanism of breaking is related

to an instability, the size of the ejecta will probably be

of the order of the wavelength of the instability, i.e. of

the order of the equilibrium thickness and not its

maximum thickness. Thus, there is no conflict with

the thickness of the film at the breaking point and the

size of the ejecta.

5.2. Constraints on bubble radius

Laboratory experiments show that in well-devel-

oped slug flow, bubbles occupy a large portion of the

conduit (Jaupart and Vergniolle, 1988, 1989). Conse-

quently, unless the shape of the conduit changed

significantly during the eruption, it is reasonable to

expect that the bubble radius would remain approxi-

mately constant throughout the 1999 eruption.

Synthetic waveforms modelling Shishaldin bub-

bles suggest that all of the bubbles have a radius of

c 5 m. A bubble radius of 5 m, and a conduit of 6 m,

is supported by observations of the top of the Shish-

aldin conduit. Photographs taken in August 1999 and

July 2003, during overflights of the vent (Fig. 5) show

the top of a vertically walled conduit, the radius of

which is estimated to be c 12–15 m. In the latter

flight, the shadow of the helicopter on the crater wall

was used as a measuring tool to constrain the vent

radius. In both instances, only the top several meters

can be seen in the photo (Fig. 5), but we assume that it

tapers at depth and has a funnel shape as most of the

observed vents (Sparks et al., 1997). Our estimate of a

6 m radius is also consistent with direct observations

of active vents at Etna volcano, 1–5 m (Le Guern et

al., 1982; Calvari et al., 1994; Coltelli et al., 1998;

Vergniolle, 2003) and at Kilauea volcano (c 10 m;

Richter et al., 1970; Wolfe et al., 1987) and is larger

than that seen at Stromboli volcano (c 1 m; Chouet et

al., 1974). Thus, a conduit radius of c 6 m seems

reasonable for Shishaldin.

The conduit radius Rc can also be estimated from

the initial bubble radius Ro and from the thickness d of

the magma present between the bubble and the solid

wall, called the lateral film. If we assume that the

Fig. 9. Sensitivity analysis for various equilibrium thickness, heq = 0.3 m for the right column, heq = 0.2 m for the middle column, heq = 0.1 m for

the left column. Acoustic pressure is displayed on the top graphs and ratio between magma thickness and bubble radius R0 on the bottom graphs.

Note that the two graphs on the three top diagrams correspond to the cases shown in the graph below. The right column corresponds to bubble

radius R0 = 2.5 m, length L= 10 m and bubble overpressure DP= 0.9 MPa. For the middle column, R0 = 4 m, L= 16 m and DP= 0.29 MPa. In the

left column, R0 = 6 m, L= 40 m and DP= 0.075 MPa. Note that there is hardly any difference in acoustic pressure relative to reference case,

R0 = 5 m, L= 24 m and DP= 0.15 MPa, heq = 0.15 m.

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134 123

thickness d has reached its asymptotic value dl, it can

be calculated as (Batchelor, 1967):

dl ¼ 0:9Rc

l2

q2liqR

3cg

!1=6

: ð14Þ

For a magma viscosity of 500 Pa s and a bubble

radius of 5 m, the vertical film dl around each bubble

is c 0.86 m (Eq. (14)). Because the asymptotic value

dl is seldom attained even for long bubbles (Fabre

and Linne, 1992) and corresponds to a minimum

value, the conduit radius can be safely estimated at

c 6 m from acoustic measurements.

We propose that the bubble radius is constant since

we assume that the bubble volume fills the width of the

tube and there is only one active vent at the summit

(Fig. 5). The fairly well peaked frequency range during

the whole of the eruption supports this assumption. If

we suppose that the thickness of the magma above the

bubble is constant and equal to 0.15 m, the measured

waveform can be matched by a bubble radius, length

and overpressure of respectively 4 m, 27 m and 0.18

MPa or by a bubble with radius of a 6 m, 22 m and 0.13

MPa overpressure (Fig. 10).

Enlarging the possible range of values for the initial

bubble radius makes the radial oscillations of the

bubble unlikely. When using these two extreme con-

ditions for the bubble radius, the gas volume at atmo-

spheric pressure is known with an accuracy better than

F 20%. Therefore, a bubble radius of 5 m generates the

best synthetic waveforms regardless of when the signal

is chosen during the two Strombolian phases. The

uncertainties on the bubble radius are probably around

1 m at most if we suppose that the thickness heq of

magma above the bubble is properly determined.

Fig. 10. Sensitivity analysis for various bubble radius R0 = 4 m for the right column, R0 = 6 m for the left column. Acoustic pressure is displayed

on the top graphs and ratio between magma thickness and bubble radius R0 on the bottom graphs. All the graphs corresponds to a constant

equilibrium thickness, heq = 0.15 m and a magma viscosity of 500 Pa s. The right column corresponds to bubble length L= 27 m and bubble

overpressure DP= 0.18 MPa. In the left column, L= 22 m and DP= 0.13 MPa. Note that there is hardly any difference in acoustic pressure

relative to the reference case, R0 = 5 m, L= 24 m and DP= 0.15 MPa, heq = 0.15 m.

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134124

5.3. Constraints on bubble length

When a long bubble breaks, such as during a

Strombolian explosion, the duration of gas expulsion

depends on the gas velocity and the bubble length. If

the gas is expelled at a velocity deduced from height

measurements (c 50 m/s), a 100-m long bubble could

produce sound for 2 s, which could be measured on

acoustic records. However, the sound produced by a

steady gas jet carrying solid fragments is a dipolar

source, which radiates sound with less efficiency than a

monopole source such as a Strombolian explosion

(Woulff and McGetchin, 1976). It is even worse in

term of sound radiation if the sound is produced by a

gas phase free of solid fragments, a quadrupole source

resulting of turbulence in the gas jet itself. Measure-

ments of acoustic pressure, recorded at 6.5 km from the

vent and with potentially some wind, do not show any

sign of an signal induced by the gas jet itself. Therefore,

no constraint can be provided on bubble length.

6. Main results

6.1. Bubble length and overpressure

It is now possible to look at the evolution of bubble

characteristics during the two Strombolian phases to

constrain the dynamics of the eruption.

The first Strombolian phase (April 19, 1999), which

occurs almost immediately after the Subplinian phase,

displays no noticeable time evolution in bubble length

or overpressure (Fig. 11). Although the bubbles are

long (82F 11 m), their lengths are less than 20 times

the bubble radius, as is expected for slug flow (Wallis,

1969). Bubble overpressures are relatively small,

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134 125

around 0.083F 0.03 MPa. The end of this phase is

difficult to see because acoustic signals decrease slowly

before falling below the noise level.

The second Strombolian phase (22nd and 23rd of

April 1999; Fig. 12) shows more variation than the first

(Fig. 11). Bubble lengths, between 10 and 60m, are still

less than 20 times the bubble radius. Bubble overpres-

sure during the second Strombolian phase (Fig. 12)

starts and stays at a relatively low value (0.15MPa), for

the first 17 h. It presents a peak at 1.4 MPa on the 23rd

of April between 04:40 and 10:13 h, although there is

no associated change in the number of events.

While none of these explosions was visually ob-

served, tremor amplitude at the time of the pressure

peak on April 23 was the strongest ever recorded by

AVO (Thompson et al., 2002). Although no visual

observations were made of the Strombolian explo-

sions, satellite imagery at 05:30 h shows a small ash

plume, and video taken of the Shishaldin vent at 21:30

Fig. 11. Results of synthetic waveforms on the largest explosion per 400 s

radius R0 is 5 m, magma thickness above bubble heq is 0.15 m and magma

(a) Bubble length at the surface (m). (b) Bubble overpressure at the surfa

h shows the development of another small plume.

These can be either the combined effects of frequently

breaking, very long, overpressurised bubbles, as

shown by the increase in surface flux c 6000 m3/s

(Fig. 15) or proper ash plumes, as shown developing

during the pre-Subplinian and the Subplinian phases

(Vergniolle and Caplan-Auerbach, 2004b,c).

Here, we propose that the peak in overpressure

corresponds to large Strombolian bubbles rising

through a gas-rich magma. Laboratory experiments

show that under different conditions in the reservoir, a

variable quantity of small bubbles is released in the

conduit (Fig. 13), which depends on the foam dynam-

ics at the top of the reservoir and its lateral spreading.

When the latter is relatively strong, the liquid in the

tube is very rich in small bubbles, which rise as an

annular curtain of small bubbles (Fig. 13c).

The consequence is that the apparent viscosity of a

bubbly magma is much greater than the viscosity of a

during the first Strombolian phase of the 19th of April 1999. Bubble

viscosity l is 500 Pa s. Time t = 0 is 18:00 h on 19/04/1999 (UTC).

ce (� 0.1 MPa).

Fig. 12. Results of synthetic waveforms on the largest explosion per 800 s during the second Strombolian phase of the 22nd and 23rd of April

1999. Bubble radius R0 is 5 m, magma thickness above bubble heq is 0.15 m and magma viscosity l is 500 Pa s. Time t = 0 is 12:00 h on 22/04/

1999 (UTC). (a) Bubble length at the surface (m). (b) Bubble overpressure at the surface (� 0.1 MPa).

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134126

magmawithout bubbles (Jaupart andVergniolle, 1989).

Since the large bubbles of the Strombolian phase come

from the depth of the reservoir and are formed with an

initial overpressure, their final overpressure at the

surface strongly depends on the viscosity of themixture

in which they are rising (Vergniolle, 1998).

The average bubble length, during the second

Strombolian phase (24F 12 m) is less than a third

of the length estimated for the first Strombolian

phase. The bubble overpressure during the first 17

h of the second one (Fig. 12) is twice that recorded

during the first Strombolian phase (Fig. 11). These

differences in bubble lengths and bubble overpres-

sures support the interpretation that the first Strom-

bolian phase results from a strong decompression

induced by the Subplinian phase (Vergniolle and

Caplan-Auerbach, 2004c,d) whereas the second one

is more typical of a classical basaltic eruption with

relatively small (0.15 MPa) overpressure. The peak

in overpressure is probably the consequence of a

magma in the conduit richer in small gas bubbles as

shown in the laboratory experiments (Fig. 13c).

6.2. Gas volume and gas flux

Given bubble radius, length and overpressure dur-

ing the two Strombolian phases, it is fairly easy to

calculate the gas volume and gas flux emitted at the

surface per bubble. Gas volume and gas flux, calcu-

lated at atmospheric pressure, are fairly constant

during the first Strombolian phase and are respective-

ly 1.3� 104F 0.2� 104 and 2.9� 103F 4.1�102

m3/s (Figs. 14 and 15).

For the second Strombolian phase, we observe a

peak between 04:40 and 10:13 h UT (c 1.4� 104 m3

for gas volume ejected per bubble and c 3.8� 103 m3/

s for the gas flux) following a 17-h quiet period at

4.7� 103F 1.9� 103 and 1.0� 103F 4.7� 102 m3/s

(Fig. 15). Gas volume and gas flux average for the

whole second Strombolian phase is 0.9�104F

Fig. 13. Laboratory experiments showing that the conduit can contain a small gas volume fraction (a, b) or a relatively large gas volume fraction

with a small foam lying on the top of the liquid (c). Liquid is a silicone oil (Rhodorsil) of viscosity 0.1 Pa s (a, b) and 0.01 Pa s (c) for a gas flux

of 3.0� 10� 5 m3/s (a, b) and 1.3� 10� 5 m3/s. The conduit diameter is 4.4 cm and the number of bubbles at the base of the reservoir is 185. (a)

Foam at the top of the reservoir (white part) has started to coalesce (black part on the left-hand side) to produce a slug, i.e. a large gas bubble. (b)

Large gas bubble in the conduit, similar to classical Strombolian explosions. (c) Foam at the top of the reservoir (white part) has started to

coalesce (black part on the right-hand side) and is about to produce a large bubble, which then will migrate in a conduit rich in small bubbles.

Note that there is a permanent foam layer staying at the top of the liquid. This is the laboratory equivalent of the second Strombolian phase

during its peak in overpressure.

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134 127

0.8� 104 and 2.2� 103F 1.6� 103 m3/s. If we as-

sume that CO2 is the major component of the gas, the

mass flux is equal to 1.2� 103 and 8.7� 102 kg/s for

the first and the second Strombolian phases. Mass flux

has a minimum value of 470 and 360 kg/s in the

endmember case of a pure H2O phase.

The total gas volume is estimated by counting the

number of explosions per 400 s for the first Strombo-

lian phase and per 800 s for the second Strombolian

phase. On average one explosion occurs each 8.7 s for

the first Strombolian phase and each 12 s for the

second one (Caplan-Auerbach and McNutt, 2003).

The total gas volume ejected at atmospheric pressure

is 3.3� 107 m3 for the first Strombolian phase and

1.0� 108 m3 for the second. We have seen before that

although there are a few simplifying assumptions, the

determination of gas volume, and hence gas flux is

known with an accuracy of F 20% in the framework

proposed by the model of bubble vibration.

The number of bubbles has been estimated by

counting any bubble with acoustic pressure above the

detection limit (c 0.5 Pa). The total gas volume and

gas flux given above, were estimated using the volume

of the largest bubble and the number of events above

the detection threshold. The total volume of the small-

est detectable bubbles released at atmospheric pressure

is c 1.1�107 and c 5.0� 107m3 during the first and

second Strombolian phase. If the distribution of gas

volumes follows a gaussian law, the average gas

volume is the mean between the minimum and the

maximum gas volume, c 2.3� 107 and c 7.7� 107

m3 for the first and second Strombolian phase. Gas flux

based on thatmethod are reduced by a factor of 0.67 and

0.74 during the first and second Strombolian phases.

Note that the sensitivity, used in this paper, for the

pressure sensor is the theoretical value, 0.36 mV/Pa. If

instead we use the uncalibrated value of 0.2 mV/Pa, the

data amplitudes are multiplied by 0.56. Because the

frequency of the signal is not affected by the calibra-

tion, the bubbles have the same characteristics in size

but gas overpressure increases by 1.8. This leads to a

maximum in overpressure of 2.5 MPa for a mean

around 0.14MPa during the second Strombolian phase.

Gas volume and gas flux at the surface increase by less

than 20%. Therefore, the results present in this paper

are fairly robust, except for the gas overpressure during

Strombolian explosions, and do not rely heavily on the

exact value of the sensitivity.

7. Gas velocity from acoustic power

Thus far we have discussed a model for acoustic

measurements based on synthetic waveforms. How-

Fig. 14. First Strombolian phase: (a) gas volume ejected by the largest explosion every 400 s and calculated at atmospheric pressure (m3 s� 1)

and as mass flux (kg/s) assuming a pure CO2 phase. Bubble radius R0 is 5 m, magma thickness above bubble heq is 0.15 m and magma viscosity

l is 500 Pa s. Time t = 0 is 18:00 h the 19/04/1999 (UTC).

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134128

ever, there might be cases where the quality of

acoustic measurements or the intrinsic character of

the signal, prevent us from producing synthetic wave-

forms. We propose a new method, which overcomes

that difficulty and allows estimates of gas velocity. We

can then compare these results with the results

obtained from synthetic waveforms to validate a

simple and robust method to obtain gas velocity and

gas volume at the vent.

Eq. (6), which describes the time evolution of

bubble radius, is required to calculate gas velocity

from synthetic waveforms. The maximum velocity of

the magma layer above the bubble is found to be

c 30 m/s for the first 17 h and can reach up to 70 m/s

during the final 4-h climax (Fig. 16). This velocity is

that of the magma layer and can be smaller than the

gas velocity once the bubble has broken. Visual

observations by pilots show that ejecta reached

heights of a few hundreds of meters earlier on the

same day (Nye et al., 2002). If velocity v is simply

related to height H by v ¼ffiffiffiffiffiffiffiffiffi2gH

p(Wilson, 1980;

Sparks et al., 1997), ejecta velocity is between 45 and

70 m/s. Although visual observations were not made

at exactly the time during which the pressure sensor

recorded Strombolian explosions, there is an order-of-

magnitude agreement between explosion waveforms

and observed ejecta.

Woulff and McGetchin (1976) have suggested that

acoustic power could be used to estimate gas velocity

during volcanic eruptions. The total acoustic power, in

Watts, emitted in a half sphere of radius equal to the

distance r between the vents and the microphone, here

6.5 km, and radiated during a time interval T, is equal

to:

P ¼ pr2

qaircT

Z T

0

Apac � pairA2dt ð15Þ

where qair = 0.9 kg.m� 3 at 2850 m elevation (Batch-

elor, 1967) and c = 340 m/s is the sound speed (Light-

Fig. 15. Second Strombolian phase: (a) Gas volume ejected by the largest explosion every 400 (b) Gas flux ejected by the largest explosion

every 400 s and calculated at atmospheric pressure (m3 s� 1) and as a mass flux (kg/s) assuming a pure CO2 phase. Bubble radius R0 is 5 m,

magma thickness above bubble heq is 0.15 m and magma viscosity l is 500 Pa s. Time t = 0 is 12:00 h the 22/04/1999 explosion every 400 s and

calculated at atmospheric pressure (m3).

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134 129

hill, 1978). Acoustic power can be then easily mea-

sured from acoustic records. However, the relation-

ship between acoustic power and gas velocity depends

strongly on the source of sound, which can be

monopole, dipole or quadrupole. A monopole source,

which radiates isotropically, corresponds to a varying

mass flux without external forces or varying stress.

For a dipole source, there is a solid boundary which

provides an external force. For a quadrupole source,

there is a varying momentum flux which acts on the

flow. In each case, it is possible to calculate acoustic

power by assuming that the signal is periodic and

monochromatic with a radian frequency x and poten-

tially add the contribution of every frequency in a

simple linear way.

The source of volcanic explosions has been shown

to be a monopole (Vergniolle and Brandeis, 1994).

For a monopole source, the excess pressure depends

on the rate of mass outflow from the source, q in

equation (see Eq. (1)). If we assume monochromatic

oscillations of frequency x, q has the same dimension

as xq. The two are strictly equivalent if oscillations

are small. This simplification gives an order of mag-

nitude for acoustic power. Temkin (1981) uses the

notation Sx for the volume flux instead of the mass

flux q = qairSx used by Lighthill (1978). For a spher-

ical source of radius Rb:

Sx ¼ 4pR2bU ð16Þ

where U is the radial velocity. The coefficient 4 is to

be suppressed for a circular vent radiating acoustic

pressure by ejecting vertical gas at a varying velocity

U. By assuming small monochromatic oscillations at

frequency N, acoustic power Pm radiated in an infinite

space is:

Pm ¼ qairx2S2x

4pcð17Þ

Fig. 16. Maximum magma velocity (m/s) for each largest bubble per

800 s during the second Strombolian phase and estimated from

modelling the bubble vibration. Bubble radius R0 is 5 m, magma

thickness above bubble heq is 0.15 m and magma viscosity l is 500

Pas. Time t = 0 is 12:00 h on 22/04/1999 (UTC).

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134130

where qair is the air density and c the sound speed in

air (Temkin, 1981). The radiation of half a bubble in

half a space is equivalent to that of a spherical bubble

in infinite space (see Eq. (1)). Therefore, Pm (see Eq.

Fig. 17. Comparison between two methods of estimating velocities during

April 1999). On x-axis, velocity is calculated by the full modelling of bubb

power (Eq. (18)) using (a) the initial bubble radius R0 and (b) the equilib

(17)) corresponds to the acoustic radiation produced

by each Strombolian explosion at Shishaldin volcano.

For small monochromatic oscillations at frequency

x, the oscillatory velocity U has the same dimension

as xRb (Landau and Lifshitz, 1987). Using this

approximate value of x in Eq. (17), acoustic power

depends mainly on gas velocity U:

Pm ¼ Km

4pR2bqairU

4

cð18Þ

where Km is an empirical constant. We have just

shown that Km= 1 represents the exact solution for a

spherical source and Km= 1/16 is the value to be used

for a circular flat orifice (Vergniolle and Caplan-

Auerbach, 2004a). Our formulation (Eq. (18)) is

equivalent to equations used by Woulff and

McGetchin (1976), but adds an exact value for Km.

Note that in all the above analysis the length scale

is assumed to be the bubble radius. In theory, it should

be taken as the equilibrium radius Req (see Eq. (5)).

However, in practice, Req is unknown but can be

estimated by the minimum bubble radius R0, which

is on the order of the conduit radius. For small

oscillations, the two length scales are the same but

for mild or strong oscillations, there is a correcting

factor in Eq. (18), which accounts for the amplitude of

the second Strombolian phase (from 16:00 to 24:00 h, the 22nd of

le vibration (Eq. (6)). On y-axis, velocity is calculated from acoustic

rium radius Req.

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134 131

the oscillation. For simplicity, we estimate gas veloc-

ity using the initial bubble radius.

At Shishaldin, gas velocities are calculated from

averaging acoustic power over 1.5 s and using a

constant Km of 1 (Eq. (18)). Gas velocities estimated

from acoustic power are slightly larger (between 30

and 70 m/s) than values estimated by the full model of

bubble vibration (between 30 and 50 m/s) (Fig. 17).

The relationship between both estimates is roughly

linear with a slope of 1.4 (Fig. 17a). The spreading of

the correlation is related to the degree of non-linearity

in bubble oscillation, which is always mild. Estimates

of velocity from the exact solution of motion during

bubble vibration or from acoustic power are exactly

the same if using the equilibrium radius (Fig. 17b).

Note that velocities have only been estimated for

bubble vibration. This calculation ignores possible

accelerations effects due to the motion of hot mag-

matic gas once the bubble has burst. At Stromboli,

velocities obtained from modelling of bubble vibra-

tion are also smaller than independent estimates of gas

velocity above the vent (Weill et al., 1992; Vergniolle

and Brandeis, 1996). Therefore, although the acoustic

power method overestimates velocities during bubble

vibration if using the initial bubble radius, gas veloc-

ity, once the bubble has burst, is probably safely

estimated by using acoustic power with a constant

Km of 1.

8. Comparison with other volcanoes and

conclusion

The occurrence, at Shishaldin, of bubbles whose

length is significantly longer than the radius is similar

to Stromboli, whose bubbles have lengths between 1

and 25 m for a bubble radius of 1 m (Vergniolle and

Brandeis, 1996), and to Etna volcano, with bubble

length between 5 and 40 m for a bubble radius of 5 m

(Vergniolle, 2003). This is the trademark of a well-

developed slug flow (Wallis, 1969). Therefore, bubbles

present during the two Strombolian phases of Shishal-

din are not long enough to represent an inner gas jet,

such as that produced during fire fountains. Because no

confirmed fire fountaining episodes were observed at

Shishaldin, we feel that this estimate is robust.

Pressure could be used as a very good variable to

estimate the ‘‘strength’’ of an eruption. Although very

few measurements exist, there is a trend between large

overpressure and explosivity. Bubble overpressures

have been estimated at c 0.10 MPa at Stromboli

(Vergniolle and Brandeis, 1996) and between 0.05

MPa and 0.6 MPa at Etna (Vergniolle, 2003). Al-

though bubble overpressure at Shishaldin can be very

strong, our estimates are still on the same order of

magnitude as other strong Strombolian eruptions,

such as one recorded at Sakurajima volcano (Japan),

0.2–5 MPa (Morrissey and Chouet, 1997). Further-

more, bubble overpressure at Shishaldin is always

much smaller than estimates from explosive eruptions,

such as Mount Tokachi (Japan) in 1988 (between 0.1

and 1 MPa), Mount Ruapehu (New Zealand, between

0.2 and 5 MPa), the 1975 Ngauruhoe eruption (New

Zealand, between 5 and 6 MPa), and Mount Pinatubo

(Philippines) in 1991 (z 5 MPa) (Morrissey and

Chouet, 1997). The initial overpressure at the start

of the Mount Saint Helens eruption has been estimat-

ed at 7.5 MPa (Kieffer, 1981). The strong overpres-

sure associated with the second Strombolian phase

may explain the large amplitude of tremor observed at

the time (Thompson et al., 2002).

We next compare gas volume at Shishaldin to other

basaltic eruptions. At Shishaldin, the gas volume

ejected per bubble, c 1.3� 104 and c 1.0� 104 m3

for the first and second Strombolian phases respective-

ly, is larger than that observed at Stromboli, between 2

and 200 m3 when measured using acoustic data (Verg-

niolle and Brandeis, 1996) and between 40 and 180 m3

for one second from COSPECmeasurements (Allard et

al., 1994). Allard et al. (1994) further note that most

degassing at Stromboli occurs passively, rather than

during explosions, and this may also be true for

Shishaldin, as a gas plume is a constant presence at

the summit. At Shishaldin, gas flux ejected at atmo-

spheric pressure, probably mainly CO2, H2O and SO2,

is c 3.0� 103 m3/s for the two Strombolian phases.

COSPEC measurements, over the main summit craters

area at Etna volcano, shows that the gas flux of SO2 is

22, 2.2� 103 and 4.4� 103 m3/s for the main three

kinds of activity at Etna volcano, namely low passive

fuming, high Strombolian activity and lava fountains

paroxysm (Allard, 1997). Gas volumes expelled per

bubble at Shishaldin volcano is also larger than what is

estimated from acoustic measurements at Etna volcano,

4.7� 103F 1.7� 103 m3 (Vergniolle, 2003). The total

gas volume ejected per eruptive episode during the

S. Vergniolle et al. / Journal of Volcanology and Geothermal Research 137 (2004) 109–134132

2001 eruption of Etna volcano is c 6.2� 106 m3 for a

duration of 4 h, much less than at Shishaldin volcano,

3.3� 107 m3 for the first Strombolian phase and

1.0� 108 m3 for the second one. Fire fountains at

Kilauea volcano correspond to a gas volume at atmo-

spheric pressure between 5.0� 108 and 3.0� 109 m3

for the Pu’u O’o eruption (Vergniolle and Jaupart,

1990), which is more than 20 times that of Shishaldin.

Therefore, the large difference in gas volumes is

representative of two different eruption dynamics, such

as an inner gas jet feeding a fire fountain at a volcano

such as Kilauea or a continuous series of large bubbles

like at Shishaldin volcano.

Although Shishaldin volcano is difficult to access,

acoustic data have proved to be very valuable in

quantifying its eruption dynamics. Bubble lengths

and overpressure at the surface can be estimated from

synthetic waveforms, as well as gas velocity during

each Strombolian explosion. Acoustic pressure, which

can be easily measured close to an active volcano,

allows us to estimate physical variables, such as

pressure and velocity needed for understanding the

eruptive behaviour.

Acknowledgements

We thank Milton Garces for taking the initiative to

install a pressure sensor at Shishaldin. We are grateful

for the support of the Alaska Volcano Observatory, as

well as the insights of our colleagues, notably P.

Stelling and S.R. McNutt. We thank Dan Osborne, Jay

Helmericks, Steve Estes, Tanja Petersen and Guy

Tytgat of the Geophysical Institute, UAF for help in

retrieving and attempting to calibrate the pressure

sensor. We also thank Matthias Hort and two

anonymous reviewers whose comments greatly im-

proved the quality of this manuscript. This work was

supported by CNRS-INSU (ACI and PNRN: contri-

bution number 323) and by the French Ministere de

l’Environnement (number 122/2000). This is a IPGP

contribution number 1945.

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